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Boussinesq's equation for water waves : Asymptotics in Sector i

Charlier, Christophe LU and Lenells, Jonatan LU (2024) In Advances in Nonlinear Analysis 13(1).
Abstract

In a recent study, we showed that the large (x, t) behavior of a class of physically relevant solutions of Boussinesq's equation for water waves is described by ten main asymptotic sectors. In the sector adjacent to the positive x x -axis, referred to as Sector I, we stated without proof an exact expression for the leading asymptotic term together with an error estimate. Here, we provide a proof of this asymptotic formula.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
asymptotics, Boussinesq equation, initial value problem, Riemann-Hilbert problem
in
Advances in Nonlinear Analysis
volume
13
issue
1
article number
20240022
external identifiers
  • scopus:85198451295
DOI
10.1515/anona-2024-0022
language
English
LU publication?
yes
id
c428366a-41a8-4674-b307-d0cf918b9db3
date added to LUP
2024-11-27 15:08:33
date last changed
2025-04-04 15:13:56
@article{c428366a-41a8-4674-b307-d0cf918b9db3,
  abstract     = {{<p>In a recent study, we showed that the large (x, t) behavior of a class of physically relevant solutions of Boussinesq's equation for water waves is described by ten main asymptotic sectors. In the sector adjacent to the positive x x -axis, referred to as Sector I, we stated without proof an exact expression for the leading asymptotic term together with an error estimate. Here, we provide a proof of this asymptotic formula.</p>}},
  author       = {{Charlier, Christophe and Lenells, Jonatan}},
  keywords     = {{asymptotics; Boussinesq equation; initial value problem; Riemann-Hilbert problem}},
  language     = {{eng}},
  number       = {{1}},
  series       = {{Advances in Nonlinear Analysis}},
  title        = {{Boussinesq's equation for water waves : Asymptotics in Sector i}},
  url          = {{http://dx.doi.org/10.1515/anona-2024-0022}},
  doi          = {{10.1515/anona-2024-0022}},
  volume       = {{13}},
  year         = {{2024}},
}